Heat exchangers (LMTD) worksheet with answers

Free printable Heat exchangers (LMTD) worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
lengthT90 °C50 °C15 °C25 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 90 to 50 °C while the cold fluid heats from 15 to 25 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 50 °CTc: 15 → 25 °C
ΔTlm = K
2.Easy
lengthT90 °C60 °C20 °C55 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 90 to 60 °C while the cold fluid heats from 20 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 60 °CTc: 20 → 55 °C
ΔTlm = K
3.Medium
lengthT175 °C85 °C30 °C75 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 220 kW. The hot fluid cools from 175 to 85 °C and the cold fluid heats from 30 to 75 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 220 kWU = 500 W/(m²·K)Th: 175 → 85 °CTc: 30 → 75 °C
A = m²
4.Medium
lengthT130 °C25 °C50 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 130 °C on the outside of the tubes. Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 25 to 50 °C. The overall heat transfer coefficient is 2000 W/(m²·K). Find the heat transfer area A needed.

Ts = 130 °Cṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 50 °CU = 2000 W/(m²·K)
A = m²
5.Hard
lengthT135 °C105 °C47.94 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 135 to 105 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 135 → 105 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1000 W/(m²·K)
A = m²
6.Hard
lengthT100 °C40 °C20.05 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 100 to 40 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 100 → 40 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 45.51 K
  2. 2. ΔTlm = 24.63 K
  3. 3. A = 8.716 m²
  4. 4. A = 1.705 m²
  5. 5. A = 1.855 m²
  6. 6. A = 12.36 m²

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